Paul Finsler (born 11 April 1894, in
Heilbronn,
Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
, died 29 April 1970 in
Zurich,
Switzerland) was a German and Swiss
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
.
Finsler did his undergraduate studies at the
Technische Hochschule Stuttgart
The University of Stuttgart (german: Universität Stuttgart) is a leading research university located in Stuttgart, Germany. It was founded in 1829 and is organized into 10 faculties. It is one of the oldest technical universities in Germany with ...
,
and his graduate studies at the
University of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...
, where he received his Ph.D. in 1919 under the supervision of
Constantin Carathéodory
Constantin Carathéodory ( el, Κωνσταντίνος Καραθεοδωρή, Konstantinos Karatheodori; 13 September 1873 – 2 February 1950) was a Greek mathematician who spent most of his professional career in Germany. He made significant ...
. He studied for his
habilitation at the
University of Cologne
The University of Cologne (german: Universität zu Köln) is a university in Cologne, Germany. It was established in the year 1388 and is one of the most prestigious and research intensive universities in Germany. It was the sixth university to ...
, receiving it in 1922.
He joined the faculty of the
University of Zurich
The University of Zürich (UZH, german: Universität Zürich) is a public research university located in the city of Zürich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 f ...
in 1927, and was promoted to
ordinary professor
Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia.
Overview
Appointment grades
* (Pay grade: ''W3'' or ''W2'')
* (''W3'')
* (''W2'')
* (''W2'', ...
there in 1944.
Finsler's thesis work concerned
differential geometry, and
Finsler spaces were named after him by
Élie Cartan
Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometr ...
in 1934.
The
Hadwiger–Finsler inequality In mathematics, the Hadwiger–Finsler inequality is a result on the geometry of triangles in the Euclidean plane. It states that if a triangle in the plane has side lengths ''a'', ''b'' and ''c'' and area ''T'', then
:a^ + b^ + c^ \geq (a - b)^ ...
, a relation between the side lengths and area of a
triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, any three points, when non- colline ...
in the
Euclidean plane, is named after Finsler and his co-author
Hugo Hadwiger
Hugo Hadwiger (23 December 1908 in Karlsruhe, Germany – 29 October 1981 in Bern, Switzerland) was a Swiss mathematician, known for his work in geometry, combinatorics, and cryptography.
Biography
Although born in Karlsruhe, Germany, Hadwi ...
, as is the
Finsler–Hadwiger theorem
The Finsler–Hadwiger theorem is statement in Euclidean plane geometry that describes a third square derived from any two squares that share a vertex. The theorem is named after Paul Finsler and Hugo Hadwiger, who published it in 1937 as part o ...
on a square derived from two other squares that share a vertex. Finsler is also known for his work on the
foundations of mathematics
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathe ...
, developing a
non-well-founded set theory
Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axio ...
with which he hoped to resolve the contradictions implied by
Russell's paradox
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901. Russell's paradox shows that every set theory that contains ...
.
Publications
* (Reprinted by Birkhäuser (1951))
*
*
*
*
*Finsler: ''Aufsätze zur Mengenlehre.'' (ed. G. Unger) 1975.
*
References
Further reading
*.
{{DEFAULTSORT:Finsler, Paul
1894 births
1970 deaths
20th-century German mathematicians
Swiss mathematicians
Differential geometers
Set theorists
University of Stuttgart alumni
University of Göttingen alumni
University of Cologne alumni
University of Zurich faculty
People from Heilbronn
German emigrants to Switzerland